hello everyone....im really hoping someone can help me, im in somewhat of a fix.

the problem is: x3+2x2-x-2

i have to:

find where f(x) is increasing/decreasing
where it is concave up/concave down
local max/min
and then finally sketch the curve of the graph

my first step is to take the derivative, which is : f'(x)=3x2+4x-1
im a bit lost as to what i should do after this. i know i have to find the critical points where x=0 and is undefined.
when the whole equation =0, x= -4/3? the derivative cant be further factored, right?

i cant get past this point, so any guidance is highly appreciated. thanks.

May 3rd 2013, 05:57 PM

Prove It

Re: sketching curve graph

f(x) is increasing where f'(x) > 0.
f(x) is decreasing where f'(x) < 0.
Local maxima and minima occur where f'(x) = 0. If it's a maximum then f''(x) < 0 at that point, and if it's a minimum then f''(x) > 0 at that point.

To sketch the graph, find the critical points, the x and y intercepts and then you have enough info to sketch...

May 3rd 2013, 06:14 PM

noork85

Re: sketching curve graph

yes i know that, but im stuck after getting the first derivative. i know i have to get the critical points after that but, how do i make that derivative equal 0 and get a value for it? it dosnt factor...

May 3rd 2013, 07:08 PM

hollywood

Re: sketching curve graph

To find out where 3x^2+4x-1 is zero, since it won't factor easily, use the quadratic equation....

- Hollywood

May 3rd 2013, 08:05 PM

Prove It

Re: sketching curve graph

Quote:

Originally Posted by hollywood

To find out where 3x^2+4x-1 is zero, since it won't factor easily, use the quadratic equation....

- Hollywood

Use the Quadratic FORMULA :)

May 3rd 2013, 08:34 PM

noork85

Re: sketching curve graph

using the quadratic formula (just the cas calc) i got x=2 or x=-1 or x=1

You have the correct first derivative...and you should know that a quadratic has only two roots, I don't know how you obtained three. Don't use the CAS, plug into the quadratic formula, and what do you find...show your work so we can see what you did wrong if you don't get the correct roots.

where do i go from here. find at which inteervals the function is increasing/decreasing?? how do u do that with square roots? (hate them, btw)

May 3rd 2013, 09:35 PM

MarkFL

Re: sketching curve graph

You are correct...we don't always get rational roots. Now these two roots give you 3 open intervals on the real number line, and since the roots are not repeated, we know the sign of the derivative will alternate across the intervals, so I would choose the test point of zero in the middle interval. What is the sign of ? Once you have this, then you know the sign of the derivative is the opposite of this on the other two intervals. And this will tell you where the original function is increasing/decreasing. What do you find?

You have correctly used the roots of the derivative to divide the number line, but the sign associated with the leftmost interval should be positive, for the reason I cited above. If you wish to test all 3 intervals, I would use integers...-2 for the leftmost interval, 0 for the middle and 1 for the rightmost. Get decimal approximations for the roots of the derivative, and you will see why these work.

May 3rd 2013, 10:08 PM

noork85

Re: sketching curve graph

is that always the case? since f(0) is (-), then the other two intervals will always be positive?

and just to be sure, to get the signs, im plugging in numbers into the derivative or the original equation? i plugged (-1) and (1) on the left and right intervals into the derivative. but i think youre supposed to use the original, no ?

May 3rd 2013, 10:12 PM

MarkFL

Re: sketching curve graph

It is only the case when the roots are of odd multiplicity, here your two roots are both of multiplicity 1, so we know the sign will alternate.

You want to check the sign of the derivative, since a positive derivative means the original function is increasing, while a negative derivative means it is decreasing. -1 is in the same interval as 0, that's why I suggest using -2 as a test point for the leftmost interval.

May 3rd 2013, 10:25 PM

noork85

Re: sketching curve graph

okay...gotcha.

now the next step is finding the inflection point, right? how does this look?

is it an inflection point? function is increasing on both sides. (Thinking)